1813, John Farey, General View of the Agriculture of Derbyshire, v 2, ch 3, London: Board of Agriculture and Internal Improvement, p 15:

Another contrivance worth mentioning, is, the manner of conducting the water down from an Eaves-trough or Lander, which is very common about Mansfield, on the edge of Nottinghamshire; it consists, in suspending a slight wooden rod from the end of the Lander, hanging down into the Water-Butt or Cistern, down which the water runs, without being scattered by the wind, or blown against the wall, as too constantly happens, unless expensive upright spouts or trunks are used, to convey the water down, and which are very subject to decay.

e, the eave-trough, hollowed, as usual, out of solid timber, and having the outer edge an inch lower than the inner.

1851, Herman Melville, Moby-Dick, or the Whale, v 3, p 211:

They laugh at long-togs so, Flask; but seems to me, a Long tailed coat ought always to be worn in all storms afloat. The tails tapering down that way, serve to carry off the water, d'ye see. Same with cocked hats; the cocks form gable-end eave-troughs, Flask.

1870, William Wait, A Digest of New York Reports, v 2, Albany: William Gould & Son, p 1407:

Where in an action for a nuisance, in allowing the water from the defendant's roof to be shed on the plaintiff's land, there was evidence to show that the water did not run upon the plaintiff's premises until after a new eavestrough was constructed and put up, and that since that time it did run over and upon the plaintiff's premises, and injured his land; it was held, that the judge on the tiral erred in nonsuiting the plaintiff.